Elio makes candles that are $14\text{ cm}$ tall. Each candle burns $8$ hours before going out. He is wondering how many hours a $21\text{ cm}$ tall candle can burn for. He assumes that the relationship between the height of a candle and number of hours it burns $(h)$ is proportional. How long can a $21 \text{ cm}$ tall candle burn for?
Explanation: We can set up a proportion like this: $\dfrac{\text{Size of candle B}}{\text{Size of candle A}} = \dfrac{\text{Duration of candle B}}{\text{Duration of candle A}}$ Substituting values from the problem, we get this: $\dfrac{21\text{ cm}}{14\text{ cm}} = \dfrac{h\text{ hours}}{8\text{ hours}}$ Now, solve the proportion for $h$ : $\begin{aligned} \dfrac{21}{14} &= \dfrac{h}{8} \\\\ \dfrac{3}{2} &= \dfrac{h}{8} \\\\ 8 \cdot \dfrac{3}{2} &= h \\\\ \dfrac{24}{2} &= h \\\\ 12 &= h \end{aligned}$ A $21 \text{ cm}$ tall candle can burn for $12$ hours.